Answer:
x = -31/4
Step-by-step explanation:
3(2x+5) = 2(x-8)
or, 6x+15 = 2x-16
or, 6x-2x = -16-15
or, 4x = -31
or, x = -31/4
The function
gives the number of the original trout alive after x years. When the number of the original trout alive is 300, then
![300=1500e^{-0.4x}](https://tex.z-dn.net/?f=300%3D1500e%5E%7B-0.4x%7D)
Solve this equation:
![e^{-0.4x}=\dfrac{300}{1500},\\ \\e^{-0.4x}=\dfrac{1}{5},\\ \\-0.4x=\ln \dfrac{1}{5},\\ \\x=\dfrac{\ln \dfrac{1}{5}}{-0.4}\approx 4.024.](https://tex.z-dn.net/?f=e%5E%7B-0.4x%7D%3D%5Cdfrac%7B300%7D%7B1500%7D%2C%5C%5C%20%5C%5Ce%5E%7B-0.4x%7D%3D%5Cdfrac%7B1%7D%7B5%7D%2C%5C%5C%20%5C%5C-0.4x%3D%5Cln%20%5Cdfrac%7B1%7D%7B5%7D%2C%5C%5C%20%5C%5Cx%3D%5Cdfrac%7B%5Cln%20%5Cdfrac%7B1%7D%7B5%7D%7D%7B-0.4%7D%5Capprox%204.024.)
Answer: after 4.024 year (or 5 year if round to the whole number of years)
Answer:
a = 8 m
Step-by-step explanation:
Since, given is an isosceles right triangle.
So, by Pythagoras theorem:
![{a}^{2} + {a}^{2} = {(8 \sqrt{2} )}^{2} \\ \\ 2 {a}^{2} = 128 \\ \\ {a}^{2} = \frac{128}{2} \\ \\ {a}^{2} = 64 \\ \\ a = \sqrt{64} \\ \\ a = 8 \: m](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20%2B%20%20%7Ba%7D%5E%7B2%7D%20%20%3D%20%20%7B%288%20%5Csqrt%7B2%7D%20%29%7D%5E%7B2%7D%20%20%5C%5C%20%20%5C%5C%202%20%7Ba%7D%5E%7B2%7D%20%20%3D%20128%20%5C%5C%20%20%5C%5C%20%20%7Ba%7D%5E%7B2%7D%20%20%3D%20%20%5Cfrac%7B128%7D%7B2%7D%20%20%5C%5C%20%20%5C%5C%20%20%7Ba%7D%5E%7B2%7D%20%20%3D%2064%20%5C%5C%20%20%5C%5C%20a%20%3D%20%20%5Csqrt%7B64%7D%20%20%5C%5C%20%20%5C%5C%20a%20%3D%208%20%5C%3A%20m)
Answer: 45 dollars and it was a distance of 5 kilometers
Step-by-step explanation: What i did was start with 30, then keep adding 3 till i got the a multiple of 5.
30 + 3 = 33
33 + 3 = 36
36 + 3 = 39
39 + 3 = 42
42 + 3 = 45
So already i know that it is 5 kilometers, because i added 3 to 30 five times.
No i will do that with the second company
20 + 5 = 25
25 + 5 = 30
30 + 5 = 35
35 + 5 = 40
40 + 5 = 45
That is also 5 kilometers, because i added 5 to 20 five times. I also know they are the same price, because they both added to 45 dollars.
Thats how i solved it.
I really hope that helps!
2x^2 - 8x - 24
First, we can factor a 2 out of this expression to simplify it.
2(x^2 - 4x - 12)
Now, we can try factoring this two ways: by using the quadratic formula, or by using the AC method.
We're gonna try using the AC method first.
List factors of -12.
1 * -12
-1 * 12
2 * -6
-2 * 6 (these digits satisfy the criteria.)
Split the middle term.
2(x^2 - 2x + 6x - 12)
Factor by grouping.
2(x(x - 2) + 6(x - 2)
Rearrange terms.
<h3><u>(2)(x + 6)(x - 2) is the fully factored form of the given polynomial.</u></h3>